Embibe Experts Solutions for Chapter: Electrostatics, Exercise 4: Exercise-4

$2$ small balls having the same mass & charge & located on the same vertical at heights $h_1$ & $h_2$ are thrown in the same direction along the horizontal at the same velocity $v$. The $1^{\mathrm{st} }$ ball touches the ground at a distance $l$ from the initial vertical. At what height will the $2^{\mathrm{nd} }$ ball be at this instant? The air drag & the charges induced should be neglected.

A circular ring of radius $R$ with uniform positive charge density $\lambda$ per unit length is fixed in the $Y-Z$ plane with its centre at the origin $O$. A particle of mass $m$ and positive charge $q$ is projected from the point $P$ $\left(\sqrt{3}R,0,0\right)$ on the positive $X$-axis directly towards $O$, with initial velocity $v$. Find the smallest value of the speed $v$ such that the particle does not return to $P$.

Small identical balls with equal charges are fixed at vertices of regular $2009-$ go $n$ with side $a$. At a certain instant, one of the balls is released & a sufficiently long time interval later, the ball adjacent to the first released ball is freed. The kinetic energies of the released balls are found to differ by $K$ at a sufficiently long distance from the polygon. Determine the charge $q$ of each ball.

The electric field in a region is given by $\overrightarrow{E}=\frac{E_{0}x}{l}\overrightarrow{\mathrm{i}}$. Find the charge contained inside a cubical volume bounded by the surfaces $x=0, x=a, y=0, y=a, z=0 \mathrm{and} z=a$. Take $E_0=5\times {10}^3 \mathrm{N} {\mathrm{C}}^{-1},$ $l=2 \mathrm{cm} \mathrm{and} a=1 \mathrm{cm}$.

A cavity of radius $r$ is present inside a solid dielectric sphere of radius $R$, having a volume charge density of $\rho$. The distance between the centres of the sphere and the cavity is a. An electron $e$ is kept inside the cavity at angle $\theta =45°$ as shown. How long will it take to touch the sphere again?

Positive charge $Q$ is uniformly distributed throughout the volume of a sphere of radius $R$. A point mass having charge $+q$ and mass $m$ is fired towards the centre of the sphere with velocity $v$ from a point A at distance $r (r>R)$ from the centre of the sphere. Find the minimum velocity $v$ so that it can penetrate $\frac{R}{2}$ distance of the sphere. neglect any resistance other than electric interaction. Charge on the small mass remains constant throughout the motion.

Electrically charged drops of mercury fall from altitude $h$ into a spherical metal vessel of radius $R$ in the upper part of which there is a small opening. The mass of each drop is $m$ &  charge is $Q$. What is the number '$n$' of last drop that can still enter the sphere.

Consider the configuration of a system of four charges each of value $+q$. Find the work done by external agent in changing the configuration of the system from figure $\left(\mathrm{i}\right)$ to figure. $\left(\mathrm{ii}\right)$.